If y < x < 0, which of the following numbers is greatest?

Rationale

|y| is the greatest number among the options given the condition y < x < 0.

Since both y and x are negative, the absolute values |x| and |y| will be positive, and |y| will be larger than both y and x. Additionally, |y - x| is the absolute difference between two negative numbers, which cannot exceed |y|.

A (0) YOUR ANSWER

Zero is greater than any negative number, but since both y and x are less than 0, 0 is not part of the range defined by y < x. Therefore, 0 cannot be considered the greatest in this context.

B (x + y) YOUR ANSWER

The sum x + y will also be negative since both x and y are negative. Thus, it cannot be greater than |y|, which is a positive quantity in this case. Therefore, x + y will not be the greatest.

C (|x|) YOUR ANSWER

While |x| is positive, it represents the absolute value of a negative number (x), which is less than |y| as y is also negative and less than x. Hence, |x| cannot be the greatest.

D (|y|) CORRECT

As previously established, |y| is a positive value representing the magnitude of the negative number y. Since y is less than x, |y| is guaranteed to be greater than both x and y, making it the greatest option.

E (|y - x|) YOUR ANSWER

The expression |y - x| represents the distance between y and x on the number line. While it is a positive value, it is less than |y| because y is smaller than x, which means it cannot be the greatest among the options.

Conclusion

Given the constraints y < x < 0, the comparison of absolute values highlights that |y|, being the absolute value of the smaller negative number, is the greatest among the choices. Other options either remain negative or do not exceed |y|, reinforcing that |y| stands as the largest number in this scenario.

If y < x < 0, which of the following numbers is greatest?

|y| is the greatest number among the options given the condition y < x < 0.

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